Simplify the following expression: $z = \dfrac{r^2 - 10r + 16}{r - 8} $
Answer: First factor the polynomial in the numerator. $ r^2 - 10r + 16 = (r - 8)(r - 2) $ So we can rewrite the expression as: $z = \dfrac{(r - 8)(r - 2)}{r - 8} $ We can divide the numerator and denominator by $(r - 8)$ on condition that $r \neq 8$ Therefore $z = r - 2; r \neq 8$